A wave gear device has a flexspline (below, “F/S”) that is a flexible, externally toothed gear that deforms elastically; a circular spline that is a rigid, internally toothed gear; and a wave generator that is an elliptical cam. The flexspline is deformed to an ellipse by the wave generator and is meshed with the circular spline, and the meshing position of the two splines is moved by the rotation of the wave generator. A reduced rotational output that corresponds to the difference in the number of teeth of the two splines can thereby be produced from one of the splines. Wave gear devices are speed reducers characterized by small size, high torque capacity, the absence of a backlash, and other characteristics.
In general, in a drive system for positioning or the like of a load-side member using an actuator provided with a motor and a speed reducer, an encoder is attached to the motor shaft, and a semi-closed loop control system is used for controlling the load position (rotational position of the load shaft) on the basis of the motor position (rotational position of the motor shaft) obtained from the encoder. This is because the encoder often cannot be attached to the load shaft and because the theoretical resolution of the load shaft is multiplied by the reduction ratio of the resolution of the motor shaft encoder, allowing the load shaft to be controlled at high resolution. However, an “angular transmission error,” which is the difference between the actual load position and the theoretical load position of the speed reducer calculated from the motor position as a controlled amount, is created in the speed reducer by the backlash, machining errors, or the like. It is therefore difficult to control the load position with a precision comparable with the theoretical resolution of the load shaft.
In a system that uses a wave gear device as a speed reducer, the absence of a backlash can markedly reduce angular transmission errors in comparison with cases in which other speed reducers are used. However, positioning precision is adversely affected by angular transmission errors (below, “relative rotation-synchronous components”) synchronized with rotation and brought about by low gear precision, a difference between the shaft centers of the speed reducer and the load, and other fabrication errors, and angular transmission errors brought about by the non-linear elastic deformation of the flexspline. In addition, numerous analyses, modeling, and compensation methods have been reported because such error components act to excite oscillations during positioning response and other types of acceleration and deceleration, as well as non-linear torsional oscillations due to the flexibility of the wave gear device. In particular, there are many compensation methods aimed at inhibiting torsional oscillations because a large resonance is established when the cycle of the relative rotation-synchronous components coincides with the frequency of the torsional oscillation. Against this background, the present inventors have previously proposed a method for compensating for angular transmission errors that addresses the issue of static positioning precision and involves modeling the entire actuator, including the relative rotation-synchronous components in the following Document.
“Mathematical Modeling for Angular Transmission Error by Gear Accuracy of Harmonic Drive Gearing,” Tokai-Section Joint Conference of the 8 Institutes of Electrical and Related Engineers, O-140 (2007), (Tomohiro MIZUNO, Masafumi YAMAMOTO, Makoto IWASAKI, Motohiro KAWAFUKU, Hiromu HIRAI, Yoshifumi OKITSU, Kozo SASAKI, Toshio YAJIMA)